U.S. Pat. No. 4,901,839 granted Feb. 20, 1990 to Gerald E. Johnson and James A. Rivera, which is incorporated herein in its entirety, discloses an escalator, or the like conveyor, moving handrail drive which automatically increases its driving power in response to increased resistance to movement of the handrail. The handrail drive includes a pair of cooperating drive rollers which are mounted in eccentric fashion in a pair of opposed rotatable bearings. The drive rollers form a nip through which the handrail passes. As resistance to movement of the handrail increases, as when the escalator or walkway is fully loaded, frictional forces between the handrail and drive rollers increase. Increased frictional forces between the rollers and handrail causes the eccentric bearings to rotate, which moves the drive rollers closer together thus increasing nip pressure on the handrail. Copending application Ser. No. 609,285 filed Nov. 5, 1990, now U.S. Pat. No. 5,018,616, discloses an embodiment of the aforesaid handrail drive which assures balanced tightening of the handrail drive rollers.